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Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism ring. [ABSTRACT FROM AUTHOR]

We correct a mistake that occurred in the proof of the main theorem of "Singular Hochschild cohomology via singularity categories" and some inaccuracies in the proof of the reconstruction theorem. [ABSTRACT FROM AUTHOR]

Abstract We prove that derived equivalent algebras have isomorphic differential calculi in the sense of Tamarkin–Tsygan. [ABSTRACT FROM AUTHOR]

Abstract We show that the singular Hochschild cohomology (= Tate–Hochschild cohomology) of an algebra A is isomorphic, as a graded algebra, to the Hochschild cohomology of the differential graded enhancement of the singularity category of A. The existence of such an isomorphism is suggested by recent work by Zhengfang Wang. [ABSTRACT FROM AUTHOR]

Abstract Claire Amiot has classified the connected triangulated k -categories with finitely many isoclasses of indecomposables satisfying suitable hypotheses. We remark that her proof shows that these triangulated categories are determined by their underlying k -linear categories. We observe that, if the connectedness assumption is dropped, the triangulated categories are still determined by their underlying k -categories together with the action of the suspension functor on the set of isoclasses of indecomposables. [ABSTRACT FROM AUTHOR]

We prove the derived invariance of the cap product for associative algebras projective over a commutative ring. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field and A a finite-dimensional k-algebra. In this note, we determine complexes which compute the Hochschild homology of the canonical dg enhancement of the bounded derived category of A and of the canonical dg enhancement of the singularity category of A. As an application, we obtain a new approach to the computation of Hochschild homology of Leavitt path algebras. [ABSTRACT FROM AUTHOR]